9780470601983

Calculus: Single Variable, 2nd Edition

by ;
  • ISBN13:

    9780470601983

  • ISBN10:

    0470601981

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2011-01-01
  • Publisher: Wiley

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Summary

In order to show scientists and engineers how to apply calculus, this edition places a greater emphasis on conceptual understanding. It provides a nice balance between rigor and accessibility that will challenge them. Unique elements are integrated throughout that deepen the appreciation for calculus. Numerous nonstandard challenging exercises build better math skills. Innovative approaches on topics such as limits also help uncover new areas of learning for scientists and engineers.

Table of Contents

Basics
Preview
Number Systems
Planar Coordinates and Graphing in the Plane
Lines and Their Slopes
Functions and Their Graphs
Combining Functions
Trigonometry
Summary of Key Topics
Review Exercises for Chapter 1
Genesis and Development
Limits
Preview
The Concept of Limit
Limit Theorems
Continuity
Infinite Limits and Asymptotes
Limits of Sequences
Exponential and Logarithmic Functions
Summary of Key Topics
Review Exercises
Genesis and Development
The Derivative
Preview
Rates of Change and Tangent Lines
The Derivative
Rules for Differentiation
Differentiation of Some Basic Functions
The Chain Rule
Derivatives of Inverse Functions
Higher Derivatives
Implicit Differentiation
Differentials and Approximation of Functions
Other Transcendental Functions
Summary of Key Topics
Review Exercises
Genesis and Development
Applications of the Derivative
Preview
Related Rates
The Mean Value Theorem
Maxima and Minima of Functions
Applied Maximum-Minimum Problems
Concavity
Graphing Functions
L'Hopital's Rule
The Newton-Raphson Method
Antidifferentiation and Applications
Summary of Key Topics
Review Exercises
Genesis and Development
The Integral
Preview
Introduction to Integration-The Area Problem
The Riemann Integral
Properties of the Integral
The Fundamental Theorem of Calculus
A Calculus Approach to the Logarithm and Exponential Functions
Integration by Substitution
More on the Calculation of Area
Numerical Techniques of Integration
Summary of Key Topics
Review Exercises
Genesis and Development
Techniques of Integration
Preview
Integration by Parts
Powers and Products of Trigonometric Functions
Trigonometric Substitution
Partial Fractions-Linear Factors
Partial Fractions-Irreducible Quadratic Factors
Improper Integrals-Unbounded Integrands
Improper Integrals-Unbounded Intervals
Summary of Key Topics
Review Exercises
Genesis and Development
Applications of the Integral
Preview
Volumes
Arc Length and Surface Area
The Average Value of a Function
Center of Mass
Work
First Order Differential Equations-Separable Equations
First Order Differential Equations-Linear Equations
Summary of Key Topics
Review Exercises
Genesis and Development
Infinite Series
Preview
Series
The Divergence Test and The Integral Test
The Comparison Tests
Alternating Series
The Ratio and Root Tests
Introduction to Power Series
Representing Functions by Power Series
Taylor Series
Summary of Key Topics
Review Exercises
Genesis and Development
Table of Contents provided by Publisher. All Rights Reserved.

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